Asymptotic behavior of Toeplitz determinants with a delta function singularity

@article{Maric2020AsymptoticBO,
  title={Asymptotic behavior of Toeplitz determinants with a delta function singularity},
  author={Vanja Mari'c and Fabio Franchini},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={54}
}
We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener–Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited states of some integrable models, where the delta function represents a peak at the momentum of… 

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